4
Multiplication and Division Here is a forest of trees. There are 5 trees in each row, and there are 8 rows. How many trees are there in the forest altogether? If I planted 15 more trees, how many rows of 5 would I have then altogether?

6
What is 5 X 8? Does the student derive 5 x 16 = 80 by doubling 40? If the student does not derive the answers to questions (2) and (3), rate him/her at either stage 4 or 5 and proceed to the questions on proportions and ratios.

8
If the student solves any of questions (4) or (5) successfully using at least two different advanced strategies, rate him/her at stage 7 for multiplication and division and proceed to questions (6) and (7). Otherwise rate the student at stage 6.

9
Does the student use a mental part- whole strategy such as doubling? reversing with rounding and place value?

10
Does the student use mental part-whole strategies such as: standard place value? converting equivalent fractions to decimals?

12
Proportions and Ratios If the student responds incorrectly, point to the thirds. Here are 12 jelly beans to spread out evenly on top of the cake. You eat one-third of the cake. How many jelly beans do you get?

13
Proportions and Ratios Does the student use a part-whole strategy based on addition and/or multiplication? If the student cannot answer the question, allow them to manipulate the beans or counters to solve it. If the student needs to manipulate the materials to solve question (4), rate them at stage 1 or 2–4, as appropriate, and proceed to the knowledge questions.

14
For students who are unsuccessful at question (10), rate them at either stage 5 or 6, whatever is appropriate from their response to question (9), and proceed to the knowledge questions.

15
Does the student use a part-whole strategy based on equivalent fractions such as finding relationships between different units?

16
Does the student use a part-whole strategy based on equivalent fractions such as finding relationships between different units?

18
For each number I show you, tell me the number that comes just after it, the number that is one more. Also tell me the number that comes just before it, the number that is one less. Forwards and Backwards

19
Fractional Numbers Here are some fractions. Say each fraction as I show it. Put these fractions in order from smallest to largest

20
(If correct) explain why one-quarter is less than one-third? If the student can recognise the unit fractions but cannot order them, rate him/her at stage 4. Explain how you know this. If the student orders unit fractions but cannot recognise that is equivalent to 1 or 1, rate him/her at stage 5.

21
Here are some fractions. Put them in order from smallest to largest. Does the student recognise the equivalence of two-thirds and six-ninths? If so, rate them at stage 7 at least, if not rate them at stage 6. Rate a student who successfully orders all the fractions in question (20) at stage 8.

23
Place Value For the following questions, students should be rated by their fluent recall. Prolonged use of strategising suggests the student does not know the answer, and must work it out. The student must correctly answer all of questions... (21) and (22) to be rated at stage 5, otherwise rate them at stage 4. (23) and (24) to be rated at stage 6, (25) and (26) to be rated at stage 7, (27) to (30) to be rated at stage 8. Where the student shows knowledge gaps, rate him/her at the previous stage.